A state observer for nonlinear delay systems

The problem of state reconstruction from input and output measurements for nonlinear time delay systems is studied in this paper and a state observer is proposed that is easy to implement and, under suitable assumptions on the system and on the input function, gives exponential observation error decay. The proposed observer is itself a delay system and can be classified as an identity observer, in that it is such that if at a given time instant the system and observer states coincide, on a suitable Hilbert space, the observation error remains zero in all following time instants. The computation of the feedback gain is very straightforward. A sketch of convergence proof is presented in the paper and simulations are reported that show the high effectiveness of the proposed observation algorithm.